Diversity calculation
Masatoshi Katabuchi
2021/11/9
Course materials for 2021-11-9 AFEC at XTBG.
1 Prerequisites
Did you install picante and FD?
install.packages("picante")
install.packages("FD")It’s better if you have those packages too.
install.packages("tidyverse")
install.packages("rmarkdown")
install.packages("DT")Load packages.
library(picante)
library(FD)
library(tidyverse)
library(rmarkdown)2 Data
2.1 Community
samp <- read_csv("./data/samp.csv")
DT::datatable(samp)samp_mat <- as.matrix(samp[, -1])
rownames(samp_mat) <- samp$Site
samp_mat## Illicium_macranthum Manglietia_insignis Michelia_floribunda
## Site1 1 0 0
## Site2 1 2 2
## Site3 1 0 0
## Site4 1 1 0
## Site5 1 0 0
## Beilschmiedia_robusta Neolitsea_chuii Lindera_thomsonii
## Site1 0 0 0
## Site2 2 0 0
## Site3 0 0 2
## Site4 0 0 2
## Site5 0 1 1
## Actinodaphne_forrestii Machilus_yunnanensis
## Site1 0 0
## Site2 0 0
## Site3 2 2
## Site4 2 0
## Site5 0 02.2 Phylogeny
phylo <- read.tree("./data/dummy_tree.newick")
plot(phylo)
2.3 Traits
| Abbreviation | Trait | Unit |
|---|---|---|
| LMA | Leaf mass per area | g m-2 |
| LL | Leaf lifespans (longevity) | months |
| Amass | Maximum photosynthetic rates per unit mass | nnoml g-1 s-1 |
| Rmass | Dark resperation rates per unit mass | nnoml g-1 s-1 |
| Nmass | Leaf nitrogen per unit mass | % |
| Pmass | Leaf phosphorus per unit mass | % |
| WD | Wood density | g cm-3 |
| SM | Seed dry mass | mg |
trait <- read_csv("./data/dummy_trait.csv")
# trait <- read.csv("./data/dummy_trait.csv") is fine too.
DT::datatable(trait)2.4 Check how traits look like first
trait_long <- trait |>
pivot_longer(LMA:SM, names_to = "trait")
trait_long## # A tibble: 616 × 3
## sp trait value
## <chr> <chr> <dbl>
## 1 Acer_campbellii LMA 39.8
## 2 Acer_campbellii LL 7.08
## 3 Acer_campbellii Amass 985.
## 4 Acer_campbellii Rmass 54.7
## 5 Acer_campbellii Nmass 6.56
## 6 Acer_campbellii Pmass 0.42
## 7 Acer_campbellii WD 0.46
## 8 Acer_campbellii SM 0.39
## 9 Actinodaphne_forrestii LMA 69.2
## 10 Actinodaphne_forrestii LL 12.5
## # … with 606 more rowsggplot(trait_long, aes(x = value)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")
Probably we can do log-transformation for all the traits except for WD.
trait2 <- trait |>
mutate(logLMA = log(LMA),
logLL = log(LL),
logAmass = log(Amass),
logRmass = log(Rmass),
logNmass = log(Nmass),
logPmass = log(Pmass),
logSM = log(SM)) |>
dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)
DT::datatable(trait2)trait2 |>
pivot_longer(logLMA:logSM, names_to = "trait") |>
ggplot(aes(x = value)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")
3 First-order metrics (without phylogeny or traits)
3.1 Species richness, Beta diversity metrics
Skip
3.2 Nonmetric Multidimensional Scaling (NMDS)
res_mds <- metaMDS(samp_mat)## Run 0 stress 0
## Run 1 stress 0
## ... Procrustes: rmse 0.02526493 max resid 0.03292858
## Run 2 stress 0
## ... Procrustes: rmse 0.07460072 max resid 0.1212224
## Run 3 stress 7.702795e-05
## ... Procrustes: rmse 0.1288683 max resid 0.1986258
## Run 4 stress 8.399882e-05
## ... Procrustes: rmse 0.1450585 max resid 0.2619662
## Run 5 stress 0.09680968
## Run 6 stress 0
## ... Procrustes: rmse 0.06406709 max resid 0.09894247
## Run 7 stress 0
## ... Procrustes: rmse 0.05027182 max resid 0.06478723
## Run 8 stress 0
## ... Procrustes: rmse 0.05059059 max resid 0.09076615
## Run 9 stress 0
## ... Procrustes: rmse 0.04645115 max resid 0.06630074
## Run 10 stress 0
## ... Procrustes: rmse 0.04404698 max resid 0.07108026
## Run 11 stress 0
## ... Procrustes: rmse 0.1055728 max resid 0.146155
## Run 12 stress 0
## ... Procrustes: rmse 0.1075069 max resid 0.1667785
## Run 13 stress 0
## ... Procrustes: rmse 0.08572715 max resid 0.1265407
## Run 14 stress 6.957901e-05
## ... Procrustes: rmse 0.1124032 max resid 0.1765896
## Run 15 stress 0.144516
## Run 16 stress 0
## ... Procrustes: rmse 0.06685675 max resid 0.1069597
## Run 17 stress 9.128867e-05
## ... Procrustes: rmse 0.1288646 max resid 0.198633
## Run 18 stress 0.1302441
## Run 19 stress 0.2297529
## Run 20 stress 7.291967e-05
## ... Procrustes: rmse 0.1229564 max resid 0.184164
## *** No convergence -- monoMDS stopping criteria:
## 16: stress < smin
## 1: stress ratio > sratmax
## 3: scale factor of the gradient < sfgrminplot(res_mds)
We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sense.
ordiplot(res_mds, type = "n")
orditorp(res_mds, display = "species", col = "red", air = 0.01)
orditorp(res_mds, display = "sites", cex = 1.25, air = 0.01)
4 Phylogenetic metrics
4.1 Branch length based metric
4.1.1 PD
res_pd <- pd(samp_mat, phylo)
res_pd## PD SR
## Site1 1.000000 1
## Site2 3.022727 4
## Site3 2.909091 4
## Site4 3.136364 4
## Site5 2.454545 3You can always see the help.
?pd4.2 Distance based metric
cophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.
cophenetic(phylo)[1:5, 1:5]## Acer_campbellii Melia_toosendan Skimmia_arborescens
## Acer_campbellii 0.0000000 0.18181818 0.18181818
## Melia_toosendan 0.1818182 0.00000000 0.09090909
## Skimmia_arborescens 0.1818182 0.09090909 0.00000000
## Rhus_sylvestris 0.3636364 0.36363636 0.36363636
## Sterculia_nobilis 0.5454545 0.54545455 0.54545455
## Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii 0.3636364 0.5454545
## Melia_toosendan 0.3636364 0.5454545
## Skimmia_arborescens 0.3636364 0.5454545
## Rhus_sylvestris 0.0000000 0.5454545
## Sterculia_nobilis 0.5454545 0.00000004.2.1 MPD
\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j
res_mpd <- mpd(samp_mat, cophenetic(phylo))
res_mpd## [1] NA 1.568182 1.454545 1.606061 1.636364The above vector shows MPD for each site.
4.2.2 MNTD
\(MNTD = \frac{1}{n} \Sigma^n_i min \delta_{i,j} \; i \neq j\), where \(min \delta_{i, j}\) is the minimum distance between species i and all other species in the community.
res_mntd <- mntd(samp_mat, cophenetic(phylo))
res_mntd## [1] NA 1.181818 1.181818 1.295455 1.2727275 Functional metrics
5.1 Community weighted means (CWM)
\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]
tmp <- trait2 |>
filter(sp %in% colnames(samp_mat))
tmp## # A tibble: 8 × 9
## sp logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Actinodaphne_f… 4.24 2.53 5.01 2.17 0.412 -1.83 0.48 0.300
## 2 Beilschmiedia_… 3.61 3.09 5.72 3.53 1.75 -1.35 0.47 0.770
## 3 Illicium_macra… 5.66 4.75 3.27 0.793 -0.288 -3.51 0.4 -0.0305
## 4 Lindera_thomso… 4.47 3.70 5.49 3.02 0.626 -3.00 0.53 -0.734
## 5 Machilus_yunna… 4.26 3.36 4.65 2.69 0.239 -0.821 0.59 0.0770
## 6 Manglietia_ins… 6.22 5.24 3.10 0.255 -0.431 -3.91 0.45 -0.0513
## 7 Michelia_flori… 4.93 3.99 3.65 2.00 0.457 -3.91 0.54 0.621
## 8 Neolitsea_chuii 4.65 4.18 5.20 2.30 0.489 -2.12 0.43 -1.71(ab <- apply(samp_mat, 1, sum))## Site1 Site2 Site3 Site4 Site5
## 1 7 7 6 3# inner product
(CWS <- samp_mat %*% as.matrix(tmp[,-1]))## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.4121097 -1.832581 0.48
## Site2 31.729450 25.585161 33.973907 16.848875 4.5974297 -17.531309 3.28
## Site3 35.828159 29.342331 28.910240 11.266140 1.4425535 -21.721201 3.32
## Site4 30.140733 24.069613 24.233478 10.201674 2.2197972 -18.827747 2.93
## Site5 14.713415 11.128090 12.759265 5.116104 0.2203436 -6.565585 1.52
## logSM
## Site1 0.3001046
## Site2 0.3114643
## Site3 -1.9909259
## Site4 2.2087792
## Site5 0.3257723(CWM <- CWS / ab)## logLMA logLL logAmass logRmass logNmass logPmass WD
## Site1 4.236712 2.527327 5.006359 2.173615 0.41210965 -1.832581 0.4800000
## Site2 4.532779 3.655023 4.853415 2.406982 0.65677568 -2.504473 0.4685714
## Site3 5.118308 4.191762 4.130034 1.609449 0.20607908 -3.103029 0.4742857
## Site4 5.023456 4.011602 4.038913 1.700279 0.36996620 -3.137958 0.4883333
## Site5 4.904472 3.709363 4.253088 1.705368 0.07344788 -2.188528 0.5066667
## logSM
## Site1 0.3001046
## Site2 0.0444949
## Site3 -0.2844180
## Site4 0.3681299
## Site5 0.10859085.2 Distance based metrics
5.2.1 Prepare a trait distance matrix
We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.
trait_mat0 <- as.matrix(trait2[, -1])
rownames(trait_mat0) <- trait2$spLet’s see a subset of the trait matrix
trait_mat0[1:5, 1:5]## logLMA logLL logAmass logRmass logNmass
## Acer_campbellii 3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis 4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans 4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta 3.614964 3.085573 5.722441 3.526655 1.7544037Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.
Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))
trait_mat <- scale(trait_mat0)
par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])
par(mfrow = c(1, 1))Now we can make a trait distance matirx.
trait_dm <- as.matrix(dist(trait_mat))Let’s see the first 5 species.
trait_dm[1:5, 1:5]## Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis
## Acer_campbellii 0.000000 3.799360 5.216902
## Actinodaphne_forrestii 3.799360 0.000000 2.415031
## Alnus_nepalensis 5.216902 2.415031 0.000000
## Anneslea_fragrans 3.175911 2.335392 3.225141
## Beilschmiedia_robusta 2.545269 2.565063 3.638183
## Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii 3.175911 2.545269
## Actinodaphne_forrestii 2.335392 2.565063
## Alnus_nepalensis 3.225141 3.638183
## Anneslea_fragrans 0.000000 1.579930
## Beilschmiedia_robusta 1.579930 0.0000005.2.2 MPD
mpd(samp_mat, trait_dm)## [1] NA 4.288349 3.530805 3.961248 3.438008ses.mpd(samp_mat, trait_dm)## ntaxa mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank mpd.obs.z
## Site1 1 NA NaN NA NA NA
## Site2 4 4.288349 3.718916 0.7982242 770 0.7133754
## Site3 4 3.530805 3.710853 0.7800160 443 -0.2308267
## Site4 4 3.961248 3.677795 0.7798205 665 0.3634857
## Site5 3 3.438008 3.712299 1.0317794 447 -0.2658423
## mpd.obs.p runs
## Site1 NA 999
## Site2 0.770 999
## Site3 0.443 999
## Site4 0.665 999
## Site5 0.447 9995.2.3 MNTD
mntd(samp_mat, trait_dm)## [1] NA 2.504352 2.697074 1.873825 2.6135855.3 Branch length based metric
5.3.1 FD
We will make a functional dendrogram using clustring methods. We use UPGMA in this example.
t_clust <- hclust(dist(trait_mat), method = "average")
plot(t_clust)
5.3.2 More functional diversity metrics
res_fd <- dbFD(trait_mat[colnames(samp_mat), ], samp_mat)## FEVe: Could not be calculated for communities with <3 functionally singular species.
## FDis: Equals 0 in communities with only one functionally singular species.
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species.
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed.
## FRic: Quality of the reduced-space representation = 0.811349
## FDiv: Could not be calculated for communities with <3 functionally singular species.res_fd## $nbsp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $sing.sp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $FRic
## Site1 Site2 Site3 Site4 Site5
## NA 5.453089 2.917904 3.000656 3.553247
##
## $qual.FRic
## [1] 0.811349
##
## $FEve
## Site1 Site2 Site3 Site4 Site5
## NA 0.7595456 0.6769400 0.7085376 0.7584941
##
## $FDiv
## Site1 Site2 Site3 Site4 Site5
## NA 0.7301943 0.7617251 0.9166699 0.8261683
##
## $FDis
## Site1 Site2 Site3 Site4 Site5
## 0.000000 2.710994 1.842262 2.311159 2.042416
##
## $RaoQ
## Site1 Site2 Site3 Site4 Site5
## 0.000000 8.376023 4.005094 5.664467 4.379844
##
## $CWM
## logLMA logLL logAmass logRmass logNmass logPmass
## Site1 1.4467783 1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781
## Site2 0.5666449 0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119
## Site3 -0.1410729 -0.33319385 0.27087040 -0.2062427 -0.24084641 0.2088166
## Site4 0.3670613 0.03104745 0.01551229 -0.7298853 -0.34295985 -0.5718506
## Site5 0.4305791 0.56352114 0.11718014 -0.5812855 -0.29128834 -0.6020974
## WD logSM
## Site1 -1.0150179 -0.2191496
## Site2 -0.2744691 0.1665816
## Site3 0.1242879 -0.2907346
## Site4 -0.2341187 -0.3397288
## Site5 -0.4833418 -0.97019977 Computing Environment
devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.1.2 (2021-11-01)
## os macOS Big Sur 11.6
## system aarch64, darwin20.6.0
## ui unknown
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Asia/Shanghai
## date 2021-11-09
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date lib source
## abind 1.4-5 2016-07-21 [1] CRAN (R 4.1.0)
## ade4 * 1.7-17 2021-06-17 [1] CRAN (R 4.1.0)
## ape * 5.5 2021-04-25 [1] CRAN (R 4.1.0)
## assertthat 0.2.1 2019-03-21 [1] CRAN (R 4.1.0)
## backports 1.2.1 2020-12-09 [1] CRAN (R 4.1.0)
## bit 4.0.4 2020-08-04 [1] CRAN (R 4.1.0)
## bit64 4.0.5 2020-08-30 [1] CRAN (R 4.1.0)
## broom 0.7.8 2021-06-24 [1] CRAN (R 4.1.0)
## bslib 0.2.5.1 2021-05-18 [1] CRAN (R 4.1.0)
## cachem 1.0.5 2021-05-15 [1] CRAN (R 4.1.0)
## callr 3.7.0 2021-04-20 [1] CRAN (R 4.1.0)
## cellranger 1.1.0 2016-07-27 [1] CRAN (R 4.1.0)
## cli 3.0.0 2021-06-30 [1] CRAN (R 4.1.0)
## cluster 2.1.2 2021-04-17 [2] CRAN (R 4.1.2)
## colorspace 2.0-2 2021-06-24 [1] CRAN (R 4.1.0)
## crayon 1.4.1 2021-02-08 [1] CRAN (R 4.1.0)
## crosstalk 1.1.1 2021-01-12 [1] CRAN (R 4.1.0)
## DBI 1.1.1 2021-01-15 [1] CRAN (R 4.1.0)
## dbplyr 2.1.1 2021-04-06 [1] CRAN (R 4.1.0)
## desc 1.3.0 2021-03-05 [1] CRAN (R 4.1.0)
## devtools 2.4.2 2021-06-07 [1] CRAN (R 4.1.1)
## digest 0.6.27 2020-10-24 [1] CRAN (R 4.1.0)
## dplyr * 1.0.7 2021-06-18 [1] CRAN (R 4.1.0)
## DT 0.18 2021-04-14 [1] CRAN (R 4.1.0)
## ellipsis 0.3.2 2021-04-29 [1] CRAN (R 4.1.0)
## evaluate 0.14 2019-05-28 [1] CRAN (R 4.1.0)
## fansi 0.5.0 2021-05-25 [1] CRAN (R 4.1.0)
## farver 2.1.0 2021-02-28 [1] CRAN (R 4.1.0)
## fastmap 1.1.0 2021-01-25 [1] CRAN (R 4.1.0)
## FD * 1.0-12 2014-08-19 [1] CRAN (R 4.1.0)
## forcats * 0.5.1 2021-01-27 [1] CRAN (R 4.1.0)
## fs 1.5.0 2020-07-31 [1] CRAN (R 4.1.0)
## generics 0.1.0 2020-10-31 [1] CRAN (R 4.1.0)
## geometry * 0.4.5 2019-12-04 [1] CRAN (R 4.1.0)
## ggplot2 * 3.3.5 2021-06-25 [1] CRAN (R 4.1.0)
## glue 1.4.2 2020-08-27 [1] CRAN (R 4.1.0)
## gtable 0.3.0 2019-03-25 [1] CRAN (R 4.1.0)
## haven 2.4.1 2021-04-23 [1] CRAN (R 4.1.0)
## highr 0.9 2021-04-16 [1] CRAN (R 4.1.0)
## hms 1.1.0 2021-05-17 [1] CRAN (R 4.1.0)
## htmltools 0.5.1.1 2021-01-22 [1] CRAN (R 4.1.0)
## htmlwidgets 1.5.3 2020-12-10 [1] CRAN (R 4.1.0)
## httr 1.4.2 2020-07-20 [1] CRAN (R 4.1.0)
## jquerylib 0.1.4 2021-04-26 [1] CRAN (R 4.1.0)
## jsonlite 1.7.2 2020-12-09 [1] CRAN (R 4.1.0)
## knitr 1.33 2021-04-24 [1] CRAN (R 4.1.0)
## labeling 0.4.2 2020-10-20 [1] CRAN (R 4.1.0)
## lattice * 0.20-45 2021-09-22 [2] CRAN (R 4.1.2)
## lifecycle 1.0.0 2021-02-15 [1] CRAN (R 4.1.0)
## lubridate 1.7.10 2021-02-26 [1] CRAN (R 4.1.0)
## magic 1.5-9 2018-09-17 [1] CRAN (R 4.1.0)
## magrittr 2.0.1 2020-11-17 [1] CRAN (R 4.1.0)
## MASS 7.3-54 2021-05-03 [2] CRAN (R 4.1.2)
## Matrix 1.3-4 2021-06-01 [2] CRAN (R 4.1.2)
## memoise 2.0.0 2021-01-26 [1] CRAN (R 4.1.0)
## mgcv 1.8-38 2021-10-06 [2] CRAN (R 4.1.2)
## modelr 0.1.8 2020-05-19 [1] CRAN (R 4.1.0)
## munsell 0.5.0 2018-06-12 [1] CRAN (R 4.1.0)
## nlme * 3.1-152 2021-02-04 [1] CRAN (R 4.1.0)
## permute * 0.9-5 2019-03-12 [1] CRAN (R 4.1.0)
## picante * 1.8.2 2020-06-10 [1] CRAN (R 4.1.0)
## pillar 1.6.4 2021-10-18 [1] CRAN (R 4.1.1)
## pkgbuild 1.2.0 2020-12-15 [1] CRAN (R 4.1.0)
## pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.1.0)
## pkgload 1.2.1 2021-04-06 [1] CRAN (R 4.1.0)
## prettyunits 1.1.1 2020-01-24 [1] CRAN (R 4.1.0)
## processx 3.5.2 2021-04-30 [1] CRAN (R 4.1.0)
## ps 1.6.0 2021-02-28 [1] CRAN (R 4.1.0)
## purrr * 0.3.4 2020-04-17 [1] CRAN (R 4.1.0)
## R6 2.5.0 2020-10-28 [1] CRAN (R 4.1.0)
## Rcpp 1.0.6 2021-01-15 [1] CRAN (R 4.1.0)
## readr * 2.0.2 2021-09-27 [1] CRAN (R 4.1.1)
## readxl 1.3.1 2019-03-13 [1] CRAN (R 4.1.0)
## remotes 2.4.0 2021-06-02 [1] CRAN (R 4.1.0)
## reprex 2.0.0 2021-04-02 [1] CRAN (R 4.1.0)
## rlang 0.4.11 2021-04-30 [1] CRAN (R 4.1.0)
## rmarkdown * 2.9 2021-06-15 [1] CRAN (R 4.1.0)
## rprojroot 2.0.2 2020-11-15 [1] CRAN (R 4.1.0)
## rstudioapi 0.13 2020-11-12 [1] CRAN (R 4.1.0)
## rvest 1.0.0 2021-03-09 [1] CRAN (R 4.1.0)
## sass 0.4.0 2021-05-12 [1] CRAN (R 4.1.0)
## scales 1.1.1 2020-05-11 [1] CRAN (R 4.1.0)
## sessioninfo 1.1.1 2018-11-05 [1] CRAN (R 4.1.0)
## stringi 1.6.2 2021-05-17 [1] CRAN (R 4.1.0)
## stringr * 1.4.0 2019-02-10 [1] CRAN (R 4.1.0)
## testthat 3.0.3 2021-06-16 [1] CRAN (R 4.1.0)
## tibble * 3.1.5 2021-09-30 [1] CRAN (R 4.1.1)
## tidyr * 1.1.4 2021-09-27 [1] CRAN (R 4.1.1)
## tidyselect 1.1.1 2021-04-30 [1] CRAN (R 4.1.0)
## tidyverse * 1.3.1 2021-04-15 [1] CRAN (R 4.1.1)
## tzdb 0.1.2 2021-07-20 [1] CRAN (R 4.1.1)
## usethis 2.0.1 2021-02-10 [1] CRAN (R 4.1.0)
## utf8 1.2.1 2021-03-12 [1] CRAN (R 4.1.0)
## vctrs 0.3.8 2021-04-29 [1] CRAN (R 4.1.0)
## vegan * 2.5-7 2020-11-28 [1] CRAN (R 4.1.0)
## vroom 1.5.4 2021-08-05 [1] CRAN (R 4.1.1)
## withr 2.4.2 2021-04-18 [1] CRAN (R 4.1.0)
## xfun 0.24 2021-06-15 [1] CRAN (R 4.1.0)
## xml2 1.3.2 2020-04-23 [1] CRAN (R 4.1.0)
## yaml 2.2.1 2020-02-01 [1] CRAN (R 4.1.0)
##
## [1] /opt/homebrew/lib/R/4.1/site-library
## [2] /opt/homebrew/Cellar/r/4.1.2/lib/R/library